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On a Microscopic Representation of Space-Time III

  • Rolf Dahm
Article
  • 25 Downloads
Part of the following topical collections:
  1. Homage to Prof. W.A. Rodrigues Jr

Abstract

Using the Dirac (Clifford) algebra \(\gamma ^{\mu }\) as initial stage of our discussion, we summarize previous work with respect to the isomorphic 15 dimensional Lie algebra su*(4) as complex embedding of sl(2,\(\mathbb {H}\)), the relation to the compact group SU(4) as well as subgroups and group chains. The main subject, however, is to relate these technical procedures to the geometrical (and physical) background which we see in projective and especially in line geometry of \(\mathbb {R}^{3}\). This line geometrical description, however, leads to applications and identifications of line Complexe and the discussion of technicalities versus identifications of classical line geometrical concepts, Dirac’s ‘square root of \(p^{2}\)’, the discussion of dynamics and the association of physical concepts like electromagnetism and relativity. We outline a generalizable framework and concept, and we close with a short summary and outlook.

Keywords

Relativity Unification Quantum field theory Dirac theory Clifford algebra Geometry Projective geometry Line geometry Line Complex Complex geometry Congruences 

Mathematics Subject Classification

Primary 83E99 Secondary 14N99 

Notes

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Authors and Affiliations

  1. 1.beratung für ISMainzGermany

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